The library catalog is a good place to start to see what e-content is available to you in the form of books, e-journals (only some years may be available online), etc. (but NOT generally journal articles themselves). Do a Keyword, or Title Starts With search, and limit results to ONLINE under Access on the right-hand side. Browzine is a great resource for browsing e-journal content.
One may wish to install the browser extension Anywhere Access to enable access to PDFs available from the library wherever one is searching on the Web.
WorldCat, which is a catalog of the holdings of many libraries including and beyond Princeton, can help to determine if an electronic/digitized copy of a title exists (books). Results are organized by type. See tab at top for INTERNET if e-versions exist. The free version is available at worldcat.org .
See the Connect from Off Campus page for more details and instructions. This page also links to a guide that describes various tools that allow easy access to e-content that the library subscribes to, like LibKey Nomad, Google Scholar, etc.
If having problems with a specific electronic resource, can use the library chat ("Ask-a-Librarian") or e-mail email@example.com and let us know how you are accessing the resource, what browser, etc. There are a handful of databases that are not available remotely, mainly in the realm of business & finance.
One should never have to pay for anything, nor should you generally be asked to login other than via CAS authentication. If so, you may not be going in through the library. If in doubt, ASK. See "connect from off-campus" on the left for more information. Alternatively, see ASK US menu on library website to CHAT with or EMAIL the library.